Acoustic transducers with directional characteristics are useful in many applications. In particular, unidirectional microphones with their relatively large directivity factors are widely used. Most of these microphones are first order gradients which exhibit, depending on the construction details, directional characteristics described by (a+cos .theta.), where a is a constant and .theta. is the angle relative to the rotational axis. Directivity factors ranging up to four can be obtained with such systems.
The directivity may be improved by utilizing second order gradient microphones. These microphones have a directional pattern given by (a+cos .theta.)(b+cos .theta.) and yield maximum directivity fastors of nine. Wide utilization of such microphones was impeded by the more complicated design and the reduction of signal to noise when compared with the first order designs.